Mathematics

Step 1: Correlation Coefficient.
The correlation coefficient indicates the strength and direction of the relationship between two variables.
Its value always lies between -1 to +1. Hence A - III.
Step 2: Standard Deviation.
Standard deviation is considered the best measure of dispersion as it uses all data values.
Hence B - IV.
Step 3: Larger Samples.
Larger sample sizes give higher precision and more reliable estimates.
Hence C - I.
Step 4: Coefficient of Variation.
It is a relative and unitless measure of dispersion, used to compare variability across datasets.
Hence D - II.
Step 5: Conclusion.
So the correct matching is: A - III, B - IV, C - I, D - II.

Step 1: Understanding independence.
Two variables are said to be independent if the occurrence of one variable does not affect the probability distribution of the other.
Step 2: Relation with correlation.
If two variables are independent, they do not show any type of correlation, whether linear or nonlinear.
Thus, independent variables are always uncorrelated.
Step 3: Analysis of options.
- (1) Correlated: Wrong, because independence means no relation.
- (2) Uncorrelated: Correct, independence = no correlation.
- (3) Linearly correlated: Wrong, this implies a straight-line relationship, which violates independence.
- (4) Nonlinearly correlated: Wrong, because correlation of any form indicates dependence.
Step 4: Conclusion.
Therefore, two independent variables are always uncorrelated.